statistic discrete rondom variables 3x2where -c < x < c.1611. Let the probability density function of X be defined by f(x)i. Calculate the value of c so that f(x) is a probability distribution function.ii. Find the cumulative distribution function, F(x).

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Answered: 3x2 where -c < x < c. 16 11. Let the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 8E

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Average Traffic Spacing The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per flour, the probability P that the headway is at least t seconds is given by P=0.87t. a. What is the limiting value of P? Explain what this means in practical terms. b. The headway h can be calculated as the quotient of the spacing f, in feet, which is the average distance between vehicles, and the average speed v, in feet per second, of traffic. Thus, the probability that spacing is at least f feet is the same as the probability that the headway is at least f/v seconds. Use function composition to find a formula for the probability Q that the spacing is at least f feet. Note: Your formula will involve both f and v. c. If the average speed is 88 feet per second 60 miles per hour, what is the probability that the spacing between two vehicles is at least 40 feet?
Recall the given data. Quality (x) 1 2 Quality (x) 3 Total 1 2 3 Total f(1, 1) = = f(2, 1) = Meal Price (y) f(3, 1) = 1 45 36 9 Each probability f(x, y) will be calculated using the formula below. f(x, y) = number of times x and y occur at the same time total Note that the values along the bottom row and right most column will sum to 1. We are given that a total of 300 restaurants were evaluated. There are 45 instances for a quality rating of x = 1 and a meal price rating of y = 1. Use the given data to complete the table of probabilities. 2 1 42 45 300 3 Total 3 90 57 66 159 12 30 90 111 99 300 51 Meal Price (y) f(1, 2) = f(2, 1) = f(3, 2) = 2 f(1, 3) = f(2, 3) = f(3, 1) = 3 Total 1.00
Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 14 1 38 2 38 x P(X=x) 0 18 1 18 2 34 x P(X=x) 0 −310 1 110 2 15 3 1 x P(X=x) 0 0.74 1 0.0 2 0.54 x P(X=x) 0 110 1 15 2 35 x P(X=x) 0 0.18 1 0.76 2 0.0
A , B and C
Which statements below are true for a probability distribution function (pdf), f(x)? The total area under f(x) is equal to 1. f(x) is non-decreasing f(x) is a probability f(x) is non-negative x is non-negative
Show full solution.According to rainfall data collected by a laboratory during storm events, the precipitation level in inches (X) varies jointly with runoff in cubic feet per second (Y). The joint probability mass function (PMF) of both variables are given by the following Table: Y 1 2 3 10 0.05 0.15 0 20 0.1 0.25 0.25 30 0 0.1 0.1 a. What is the probability that the next storm will bring a precipitation of 2 or more inches and a runoff of more than 20 cfs?b. After a storm, a precipitation of 2 inches is measured. What is the probability that the runoff in this storm is 20 cfs or more?c. Are X and Y statistically dependent? Substantiate your answer.
Dental Insurance An insurance policy reimburses dental expense, X, up to a maximum benefit of 250. The probability density function for X is -0.004x for x 2 0 f(x) = otherwise, where c is a constant. Calculate the median benefit for this policy. Choose one of the following. (Hint: As long as the expenses are less than 250, the expenses and the benefit are equal.) Source: Society of Actuaries. (a) 161 (b) 165 (c) 173 (d) 182 (е) 250
The probability density function of a random variable X is shown in the figure below. fx (x) 3 1 k a) Find the coefficient k. b) Find and draw the distribution function of X (F,(x)). c) Find P(0 1). d) Find and draw the conditional distribution function F (x|X > 2). e) Find P(X 2).
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Stast 2.
You roll a fair six sided die repeatedly until the sum of all numbers rolled is greater than 6. Let X be the number of times you roll the die. Let F be the cumulative distribution function for X. Compute F(1), F(2), and F(7).
ACTIVITY 2: COMPUTE ME Direction: Determine each of the following areas and show this graphically. Use probability notation to your final answer. Write your answer on the space provided. 1.above z=1.46 2.below z=-0.58 3. between z=-1.8 and z=-1.95 4. Between z-0.76 and z=2.88 5. Between z=D-0.92 and z-1.75

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3x2 where -c < x < c. 16 11. Let the probability density function of X be defined by f(x) = i. Calculate the value of c so that f(x) is a probability distribution function. ii. Find the cumulative distribution function, F(x).